TABLE OF CONTENTS Piezoelectric resonators are often used on moving objects, e.g. missiles and satellites. When these objects accelerate, inertial force due to the acceleration causes initial or biasing deformations in the resonator. The resonant frequencies of a resonator with the presence of acceleration induced biasing fields are slightly different from the frequencies without the biasing fields. This effect can be used to make acceleration sensors. For resonators used for control and telecommunication, acceleration induced frequency shifts need to be minimized. The requirements for military applications are driving the need to advance from the ? ?/ ? 0<10 ? 10 per g production technology available today to 10 ?12 per g or better in the future. To analyze acceleration sensitivity, the theory for small fields superposed on biasing fields is needed. Early results on resonator acceleration sensitivity were given in [86 89]. More references can be found in two review articles [90, 91]. This chapter begins with the deformation of a crystal plate under acceleration, which is the biasing deformation needed in later sections on acceleration sensitivity. Since the acceleration effect is mechanical, piezoelectric coupling is neglected.
Consider a rectangular plate of AT-cut quartz (see Fig. 8.1.1). The plate is simply supported and is under a normal acceleration.
From the classical theory of flexure [88], the boundary value problem for the deflection 
is
where we have introduced...
